Pre-Calculus

Where will a cannonball land after firing? How does a harmonograph create art? How can logarithm scales help us represent the universe? Through motivating questions and interactive graphing, you’ll learn pre-calculus without relying on memorization.

By the end of this course, you’ll have mastered the foundational skills for working with exponential equations, logarithms, conic sections, and parametric equations.

• Conic Sections: Slice a cone and open a whole new class of curves.
• Circles: Explore circles and their equations on the coordinate plane.
• Ellipses: Stretch circles into ellipses and understand the relationship between an ellipse's foci and its function.
• Parabolas: Learn different ways to define parabolic curves.
• Hyperbolas: Explore this unique conic section that comes in two pieces.
• Exponentials: It gets large (or small) faster than you might think!
• Laws for Exponents: Explore the rules for combining exponential terms by thinking about exponents as repeated multiplication.
• Exponential Growth: Discover the power of exponential growth.
• Graphs and Finance: Explore fast-growing exponential functions used to model growth in finance.
• Doomsday Scenarios: Explore what happens when populations are overtaken by doomsday infections that propagate exponentially.
• Logarithms: Invert exponentials to get these.
• Defining Logarithms: Get started with the basic ideas behind logarithms.
• Graphing Logarithms: What does a log look like when you graph it?
• Log Scales: Practice the application of log scales.
• Log Arithmetic: Add, subtract, and multiply with logarithms.
• Log Equations: Solve for x when a logarithm is involved.
• Parametric Equations: Separate the horizontal and the vertical.
• Parametric Paths on a Grid: Describe horizontal and vertical motion with equations.
• Lines: Use two equations to track a point on a line.
• Projectiles: Unleash more parametric power to hurl objects through the air.
• Pendulums: Join conic sections with parametric equations and preview trigonometry along the way.